Senate Minority Leader Mitch McConnell, R-Ky., said he doesn't see an immigration overhaul happening this year.

"I think we have an irresolvable conflict here," McConnell said. "The Senate insists on comprehensive. The House says it won't go to conference with the Senate on comprehensive and wants to look at it step by step. I don't see how you get to an outcome this year with the two bodies in such different places."

The Senate passed a bipartisan, comprehensive bill in June. But the measure was not taken up by the House with many Republicans concerned over a provision in the package providing a 13-year path to citizenship to illegal immigrants, which some saw as amnesty for those that broke the law.